PONTE VEDRA BEACH, Fla. -- Phil Mickelson is looking forward to his grouping with Tiger Woods this week at the Players Championship, a rare early-round encounter with his longtime nemesis at a tournament where they have played just a single round together.

That came in 2001, during the third round, when Woods famously holed a winding, 60-foot birdie putt on the par-3 17th green on his way to a 66 and a victory the following day.

It was during a time that Woods was at his dominant best -- the 14-time major champion went on to capture the Masters two weeks later for his fourth consecutive major title, dubbed the "Tiger Slam.''

"I don't think anybody today who wasn't there to witness it, and I don't think anybody before, will ever see that level of play again,'' Mickelson said Tuesday at TPC-Sawgrass, where the Players Championship begins on Thursday.

"It was the most remarkable golf in the history of the game, and I think unrepeatable. I think it was that good. I look at 2000 as being kind of the benchmark at the U.S. Open and being the greatest golf I've ever witnessed and I believe has ever been played.

"And it sucked to have to play against him. It really did. You look at it and say, 'How am I going to beat this?' There was a stretch there for a numbers of years that it was so impressive that it was hard to imagine that it was actually happening, that he was hitting some of the shots that he was hitting and playing that well.

"The guys today look back and they say, 'Come on, how much better could he have been?' and so forth. And it goes to show you that they weren't there to witness it.''

Woods, 42, has 79 PGA Tour victories but none since 2013 and is in the midst of a comeback from spinal fusion surgery. Mickelson, 47, won his 43rd PGA Tour title earlier this year at the WGC-Mexico Championship, his first win in more than four years.

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It's the featured pairing of all featured pairings: Tiger and Phil. Let's look at what has happened before, and what this might mean for their third -- Rickie Fowler.

The two adversaries have seen their relationship mellow over the years to the point that they played a practice round together last month at the Masters. That sort of thing never happened in the past, and the PGA Tour typically went out of its way not to group them in the first two rounds of an event.

In fact, they often were on opposite sides of the draw, with one playing early on Thursday and late Friday, the other late-early.

The last time Woods and Mickelson were in the same group was the first two rounds of the 2014 PGA Championship, where the PGA of America determines the groupings. Woods missed the cut, and Mickelson went on to finish second.

In all, they have played in the same group just 35 times, with Woods holding a slight edge in their round-by-round scores at 16-15-4. Woods' scoring average is also slightly better, 69.60 to 69.91.

Woods won five of the tournaments in which they were grouped at some point, including the 2006 PGA Championship and the 2008 U.S. Open. Mickelson won three.

"We haven't been paired together in years, and as I look at the cover of the newspaper and the pairing is on there and the excitement that's been going on around here, it gets me thinking,'' Mickelson said. "Why don't we just bypass all the ancillary stuff of a tournament and just go head-to-head and just have kind of a high-stake, winner-take-all match?

"Now I don't know if he wants a piece of me, but I just think it would be something that would be really fun for us to do, and I think there would be a lot of interest in it if we just went straight to the final round.''

In a later news conference, Woods said he's not against a winner-take-all match.

"We'll play for whatever makes him uncomfortable," Woods said.

When asked what that would be, Woods added: "We'll find out."

"Now that we have an opportunity to play against each other again on the first day when the gun blows, it's going to be fun," Woods continued. "I enjoy either competing with him on the first or second day or if it's the last day. It's always been a blast, and he's one hell of a competitor, and it's always going to be a challenge to try and beat him.''

Woods and Mickelson are playing with Rickie Fowler for the two rounds, going off the first tee at 1:52 p.m. and the 10th on Friday at 8:27 a.m.